Second order non-linear differential equation modelling

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I am having a bit of a problem while modelling a hydro-mechanical system, after a long hassle with fluid mechanics, I got this not so cute non-linear differential equation, I believe I have to linearize the equation in order to model it and I have to do so near a starting point. Here is the equation:

$$ m x''(t)=-Bx' (t)- Kx(t)+ A_c p_3 (t)$$ and

$$ (dp_3)/dt= A_c*(β/V_3) x'(t) ̇$$

substituting x'(t) in the first equation:

$$x''(t)=K_1p_3(t) - K_2p_3'(t)- K_3x(t)$$

I really hope you can help I've been battling this equation for a week now. Thanks a lot for your time Hijawi